VLSI layouts of complete graphs and star graphs

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Abstract

In this paper, we present efficient layouts for complete graphs and star graphs. We show that an N-node complete graph can be optimally laid out using ⌈N24⌉ tracks for a colinear layout, and can be laid out in N416 + o(N4) area for a 2D layout. We also show that an N-node star graph can be laid out in N216 + o(N2) area, which is smaller than any possible layout of a similar-size hypercube. This solves an open question posed by Akers and Krishnamurthy in 1986. Both the layouts of complete graphs and star graphs are optimal within a factor 1 + o(1).

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